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Our experiences differ. I have found in all cases that when pure 12ths are tuned (except with wacko wound strings...) wide double octaves and narrow triple octaves are the result. The single octaves progress from 6:3 (or wider) in the bass to 4:2 in the middle and between 4:2 and 2:1 higher up. Where these changes occur depends on the scaling. Generally a studio upright will have 4:2 octaves in the temperment, a spinet between 2:1 and 4:2 in the temperment and a decent sized grand between 4:2 and 6:3 in the temperment. I have also analyzed these relationship mathematically and it confirms what I hear. OK, so you hear something different.

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Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

You are right. In general, higher octaves are taught to be tuned less narrow, 2:1 for example in the treble, because the higher coincidental partial, 4:2 and 6:3, are so faint that their beating is not heard, hence the 2:1 sounds good by itself.

However, it is not just the quality of the octave we should concern ourselves with. These higher notes must be in tune with the lower intervals. I concentrate on those intervals so the undamped treble strings ring sympathetically with the lower intervals. So the actual size of the octaves does not concern me. The byproduct of my approach is not just less narrow octaves on top, but consistently less narrow by the same amount, each one.

My checks use M3, M6, M17, m3, m6. So when comparing to lower interval beats which were all set even, all the higher ones beat even as well. See? I don't try for even M17 for example, they just happen. Trying for even M17 is putting the cart before the horse. You can get even M17 and bad compound octaves for example.

As for pure 12ths creating wide double octaves and narrow triple octaves, that is not what I've found. The pure 12th creates wide double octaves and slightly wide triple octaves. Tempering the 12th creates less wide double octaves (beatless) and pure triple octaves. I am working on a proof for that and will post it if I figure it out.

You said you have already figured this out mathematically. Can you post your proof?

You are right. In general, higher octaves are taught to be tuned less narrow, 2:1 for example in the treble, because the higher coincidental partial, 4:2 and 6:3, are so faint that their beating is not heard, hence the 2:1 sounds good by itself.

However, it is not just the quality of the octave we should concern ourselves with. These higher notes must be in tune with the lower intervals. I concentrate on those intervals so the undamped treble strings ring sympathetically with the lower intervals. So the actual size of the octaves does not concern me. The byproduct of my approach is not just less narrow octaves on top, but consistently less narrow by the same amount, each one......

If you want the undamped treble strings to ring sympathetically with the lower interals, how about pure twelfths?

Originally Posted By: Mark Cerisano, RPT

.....

As for pure 12ths creating wide double octaves and narrow triple octaves, that is not what I've found. The pure 12th creates wide double octaves and slightly wide triple octaves. Tempering the 12th creates less wide double octaves (beatless) and pure triple octaves. I am working on a proof for that and will post it if I figure it out.

You said you have already figured this out mathematically. Can you post your proof?

Since you show true interest, give me a week or three to work something up. What I have is a little out of date and not really clean. I'll start a new Topic when the time comes.

To give a preview, it has to do with the partial number, the semitone span of intervals, and the iH slope. Just like the theoretical pitches do not double each octave because of iH, neither do the beatrates of intervals. The wide RBIs less than double each octave while the narrow RBIs more than double. (Ever wonder why you can use 10th and 17th so high into the treble?) The SBIs act differently depending on the iH slope and also on the stretch scheme. The 12ths are a powerful tool however they might used.

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Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

Re: pure 12ths. I used to tune pure 12ths for that reason, but recently have experimented with tempering the 12ths in favour of a cleaner double octave. Pure 12ths really do sacrifice the double octave. Also, the 12th is not the only interval that will set up sympathetic vibration. The compound octaves do as well so that is why I favour the tempered 12th; so the double octave is cleaner and rings as well.

May I suggest that we post videos or recordings to prove our thesis as opposed to mathematical treatese? It may be more palatable to the larger audience and also more convincing. I'll see what I can do.

I read through some of them. I have to be honest. As a mechanical engineer and professional musician and piano tuner, I have delved deeply into mathematics and also holistic practical performance. I have always found mathematical analysis to come up short of high level practical performance execution.

For example, your analysis uses 4:2 octaves as assumptions. Regardless of what the graphs show, 4:2 octaves are just not good enough.

Also, your assertion of always beating partials somewhere in the octave is argued by many experienced tuners, including myself, claiming that octaves can be tuned beatless. How do you explain that? Remember, I'm an engineer, I know the math, and I know the math says it isn't possible. However, as a human piano tuner, I do it every day.

My claim of being able to create in tune single, double, and triple octaves can only be proven in practice; I have to post a video proving my technique. I think then you will hear what I am talking about. Until then...

....As a mechanical engineer and professional musician and piano tuner, I have delved deeply into mathematics and also holistic practical performance. I have always found mathematical analysis to come up short of high level practical performance execution ...

....As a mechanical engineer and professional musician and piano tuner, I have delved deeply into mathematics and also holistic practical performance. I have always found mathematical analysis to come up short of high level practical performance execution ...

Mathematics is more than numbers, so math can be used in tuning. However, there is a lot of the physics that is not very clear. I talk about it a bit with a friend from my college days who went on to work at Lawrence Berkeley Lab as a mathematician, and he agrees that we both use a lot of math, but in different ways, and it is not certain who does the most useful work.

I pointed out once before that we do not even have a real accurate definition of the pitch number of a piano tone because the vibrations are not strictly periodic. That is why I said that "in tune" is a vague term.

I read through some of them. I have to be honest. As a mechanical engineer and professional musician and piano tuner, I have delved deeply into mathematics and also holistic practical performance. I have always found mathematical analysis to come up short of high level practical performance execution.

For example, your analysis uses 4:2 octaves as assumptions. Regardless of what the graphs show, 4:2 octaves are just not good enough.

Also, your assertion of always beating partials somewhere in the octave is argued by many experienced tuners, including myself, claiming that octaves can be tuned beatless. How do you explain that? Remember, I'm an engineer, I know the math, and I know the math says it isn't possible. However, as a human piano tuner, I do it every day.

My claim of being able to create in tune single, double, and triple octaves can only be proven in practice; I have to post a video proving my technique. I think then you will hear what I am talking about. Until then...

Mark:

I am mistaken. You do not show a "true interest." It seems that what you think you hear must be what everybody actually hears, but are sometimes mistaken. And since you have "delved deeply into mathematics" you do not need me to show you the proof. You can come up with your own proof. But why bother? If it does not agree with what you think you hear, the math is obviously wrong.

As I said:

Originally Posted By: UnrightTooner

..... OK, so you hear something different.

Let's leave it at that. I am not interested in some "Schwartz" comparison.

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Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

Yes, you are missing something here. I asked your permission as a matter of courtesy since you feel I do not show a "true interest" in the subject. I found your post to be a bit defensive and I didn't want to agrivate you any further.

I also feel that your 'true interest' is in the playing with of numbers and not the practical execution of the art of piano tuning. Please don't get me wrong. I do not feel that an interest in the purely mathematical aspect of piano tuning is inferior. I admire anyone who can "delve deeply" into that and come up with some interesting proofs. The proofs I am interested in are more practical and similar to the ones I've already posted. My critiques of your approach were from that perspective, and not from that of the validity of the mathematical analysis.

I hope you are ok with that and do not take the posts too personally. I have more than a true interest in this subject. It is my passion, as I know it is yours. I hope we can see the validity in each other's perspective.

I am frustrated with myself for jumping to a conclusion. I am not going to say just what it was.

Here's the thing: Through the years I have read that people hear things different than I do. And I have read that the math says one thing when I have found that it says another. And I have found that what I hear and the math that I use agree with each other.

OK, so you hear something different than my ears hear, and perhaps your math says something different than my math says, and perhaps what you hear and what your math says do not agree with each other.

Post what you like. I am confused by your courtesy.

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Jeff DeutschlePart-Time TunerWho taught the first chicken how to peck?

From A#4, I tune 4:2 or 4:2+ octaves up. All depending, from about F5 >, I start tuning & checking my 3rd and 17th, for example, F3/A3 and F3/A5 etc...and continue up as far into the treble/high treble as I can on any particular piano. Then it is single octaves up to the top, either melodic or harmonic or both.

Sometimes, I tune M6/M17ths up through the treble.

Going down from F3, I tune a 5th down, check my 4th and octave and move on down as far as the piano will allow. For single bass strings, I use a variety of techniques, once again, all depending on the piano. It may be ghosting or it may be making the notes sound as good as I can get them to sound with octave, 10th, 17th, 12th and double octave.

Ok, I admit, I use a lot of checks as I tune, I actually, as I wrote earlier, tune with my checks and check with my tune!?!

For the high treble, if it is a good quality piano, and I am tuning for a discerning client, I have begun using the chord of nature, which I think Kent Swafford is the author of.

In general, I tune whole tone tuning. I strive for as clean sounding tuning as possible, smoothing out the 12th and D8ve. I used to stretch my tunings quiet abit but now prefer as clean sounding/just tuning as the piano will allow me.

Gary, you seem to be going further and further backwards in time on the forum. Please check the date in the top right corner of the posts you are referring to - it can be a little strange to revive old conversations like this, and needs consideration.

The topic here is an interesting question for which there is no one right or wrong answer. The inharmonicity that any piano has makes it technically impossible to have all octaves be perfectly in tune. Yet, over the years, I have heard and read about many ideas for compromise that can make it seem that single, double and triple octaves are all "perfectly" in tune.

That, in fact as been for me a very long term goal: just enough width in the single and double octaves for them to be perceived as in tune but ultimately arriving at triple and even quadruple octaves which match perfectly with the fundamental.

As long ago as 1992, I tuned a piano at a PTG convention for a recital. I had a very well respected technician who was elderly even then hurriedly approach me after that recital to say, "You have done something with the octaves! I don't know what it is but I like it!"

It was a simple matter even at that time of equalizing double octaves and octave-fifths. The idea I used was so simple that it became to be known as "mindless octaves".

A few years ago now, when my ETD was in the shop for service so I had to tune entirely by ear for a while, I came up with yet another idea. Why not play all of the notes simultaneously that had their coincident partials all be on the pitch in the upper register to be tuned?

Some partial pitches would be slightly sharp, others slightly flat but there would be that one single pitch for the note being tuned that would lie exactly in the middle of all of that slight sharpness and flatness. The beats in all related intervals would literally cancel each other out.

So, I adopted this method of tuning both the temperament and extended octaves using tone clusters. Each tone cluster reveals the exact pitch for the note being tuned by exhibiting a ZERO beat! That is true, I must say, regardless of temperament, whether Equal Temperament (ET) or any Well Temperament (WT) or Meantone Temperament (MT) is chosen.

On March 9 of this year, I had the opportunity to tune a piano for a Jazz concert event to be held the next day. I used a very slightly different version of ET where all 4ths and 5ths are equalized. The choice of temperament provided the most opportune time to exhibit both perfect octave and temperament relationships.

The chords played by the pianist are complex and often deliberately and incisively dissonant. Yet, the piano sounds clear and in tune with itself, which is the goal.

The following link is still current and has been running for weeks now but will ultimately be a past "episode" among the 280 such episodes posted as pod casts on the the website of live music from my home town, Madison, Wisconsin.

If you like modern Jazz, you will find it intriguing. Even if you don't, you will hear the clarity from the Kawai RX-3 grand piano. All partials are matched perfectly for the ultimate compromise in octaves. All chords between octaves are perfectly balanced using this technique.

Here is a rare opportunity to enjoy Jazz by a cutting edge ensemble using a state of the art tuned piano. The video is also in High Definition. You get to hear interviews and discussion of the music interspersed with the music itself. The musicians are all of the highest caliber and are all music educators to one degree or another.

The following link is still current and has remained so for a number of weeks because of the very high number of accesses to it from the USA and around the world. This is how octaves on the piano should be tuned:

I listened a bit to the video Bill Bremmer posted. It seems like a decent tuning, but I would not ascribe any special significance to it. For those who might be interested, it might be an interesting comparison to the video of one of my tunings that I posted as a sample not long ago, particularly since they are similar pianos, that is, same manufacturer and size.

I listened a bit to the video Bill Bremmer posted. It seems like a decent tuning, but I would not ascribe any special significance to it. For those who might be interested, it might be an interesting comparison to the video of one of my tunings that I posted as a sample not long ago, particularly since they are similar pianos, that is, same manufacturer and size.

Thanks, BDB for the compliment. I sent the link to a film producer client of mine in Los Angeles who has me tune his piano at home (a Yamaha S6) every time I am out there. This is what he had to say:

Quote:

Good grief Bill,

The piano sounds FANTASTIC!! Clear as a bell and it completely sits in the pocket with the rest of the band. And the players on this session really are spectacular. This is the real deal!! I thoroughly enjoyed it, all of it!!

Thanks for sharing and thanks for being so ground breaking in your tuning philosophy!!!! You are making your contribution to the planet!!!

best,Randy

As I often say, I don't tune to please or impress other piano technicians, I do it for the artists and clients I serve.

Jim, I hope you will be at the convention so you can find out what it is all about. Actually, you can find out a lot more what it is not about than what it is. There will be a whole day tuning seminar with one guy taking the whole day to tune the piano. I can't imagine the long windedness and complexity of what will be offered.

There will be another where the instructor takes two periods to tune the piano. Knowing the style pf presentation, it will probably be more mystical and magical than about good, solid technique that gets the job done.

Aural tuning has become increasingly out of reach for many tuners. All of the complex checks and dizzying rapid beats are beyond what many people can handle today. But guess what? They were also beyond what 17th and 18th Century (probably 19th Century too) keyboard tuners could handle.

So, I looked for a way to simplify everything. The way the piano was tuned in that recording could be written on a half page.

To answer your question, the notes, F#4 to E5 are tuned by playing the octave, 4th & 5th below them and tuning the note to be tuned until zero beat is heard.

The notes, F5 to E6 are tuned by playing the double octave, octave-fifth and single octave while holding them with the Sostenuto pedal and tuning the note to be tuned until there is zero beat heard.

The notes from F6 to C8 are tuned by playing the triple octave, double octave-fifth, double octave, octave-fifth and single octave while holding with the Sostenuto pedal and tuning the note to be tuned until there is zero beat.

The notes from E3 to F2 are tuned similarly: octave, 4th & 5th. E2 to F1: double octave, octave-fifth and single octave using the sostenuto pedal.

The lowest Bass from A0 to E1 are tuned by playing just a single octave loudly but with the damper pedal fully open, allowing the entire rest of the piano which has been previously tuned to resonate. The not being tuned is placed at the point where there is the quietest resonance.

Even the temperament is constructed using tone clusters. Rather than complex checks, the zero beat approach gets each note right the first time, every time with no need to perform any further checks.

It also works for getting the pitch dead on to the pitch source. I used to only be able to get my pitch to measure somewhere within a cent of dead on, 0.0 but with the tone cluster approach, I can get it to read amazingly at 0.0 every time!

The high treble can be adapted for the tuning exam simply by changing the tone cluster selection. For the notes C7-B7 during a tuning exam, play the single octave and M10 below the note being tuned and tune for the least amount of resonance.

The entire idea works because of the canceling effect of any two or more sets of equal beats.

Even the temperament is constructed using tone clusters. Rather than complex checks, the zero beat approach gets each note right the first time, every time with no need to perform any further checks.

Bill, this seems to be a new development, different to your previously posted methods/sequences (e.g. ET via Marpurg, which was centered strongly around comparing the beat rate of a 4th to that of a 5th, or judging beat rates of contiguous M3s). I'd be very interested if you could elaborate somewhat on this cluster technique without the need for further checks...

I'm already using quite a bit of this in my tunings, given your previous postings on this, Stoppers aural approach to setting octaves, and the tonal goal I've been shooting for from the start.

A procedural or efficiency question:

The double and triple octave clusters are important, but I also find them time consuming to use as they require both hands on the keys...back and forth, keys-to-the-lever, keys-to-the-lever. On an upright with the lack of sostenuto makes things a bit more clumsy as well. Any comment on achieving more efficiency of movement doing this.

Stopper's aural procedure achieved the beat cancelling effect withing the span of a single octave , but I have not been able to get it working as well as the multi-octave approach you are using.

By the way, finding the place where the low bass, and even the high bass kicks the whole open damper belly into resonance is so easy it's not funny. Couples the whole instrument together into a single whole...especially on smaller instruments.

Another interesting thing about this procedure is that it uses and refers to the temperament region directly to tune the entire instrument, rather than working off of whatever accumulated error may have crept in to the usual octave-by-octave approach.